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Simplifying x2 + 2x + -0.6214 = 0 Reorder the terms: -0.6214 + 2x + x2 = 0 Solving -0.6214 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.6214' to each side of the equation. -0.6214 + 2x + 0.6214 + x2 = 0 + 0.6214 Reorder the terms: -0.6214 + 0.6214 + 2x + x2 = 0 + 0.6214 Combine like terms: -0.6214 + 0.6214 = 0.0000 0.0000 + 2x + x2 = 0 + 0.6214 2x + x2 = 0 + 0.6214 Combine like terms: 0 + 0.6214 = 0.6214 2x + x2 = 0.6214 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 0.6214 + 1 Reorder the terms: 1 + 2x + x2 = 0.6214 + 1 Combine like terms: 0.6214 + 1 = 1.6214 1 + 2x + x2 = 1.6214 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.6214 Calculate the square root of the right side: 1.273342059 Break this problem into two subproblems by setting (x + 1) equal to 1.273342059 and -1.273342059.Subproblem 1
x + 1 = 1.273342059 Simplifying x + 1 = 1.273342059 Reorder the terms: 1 + x = 1.273342059 Solving 1 + x = 1.273342059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.273342059 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.273342059 + -1 x = 1.273342059 + -1 Combine like terms: 1.273342059 + -1 = 0.273342059 x = 0.273342059 Simplifying x = 0.273342059Subproblem 2
x + 1 = -1.273342059 Simplifying x + 1 = -1.273342059 Reorder the terms: 1 + x = -1.273342059 Solving 1 + x = -1.273342059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.273342059 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.273342059 + -1 x = -1.273342059 + -1 Combine like terms: -1.273342059 + -1 = -2.273342059 x = -2.273342059 Simplifying x = -2.273342059Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.273342059, -2.273342059}
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